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C₂×#12713 #493407

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

3424 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

(1,2);(3,4)(5,14)(6,18,20,11)(7,12)(8,13)(9,15,25,30)(10,19,26,21)(16,23)(17,28)(22,27)(24,29,34,31)(32,33);(3,5,8,17)(4,9,13,25)(6,15,20,30)(7,16,22,32)(10,23,26,33)(11,14,18,28)(12,24,27,34)(19,29,21,31);(3,6)(4,10)(5,15)(7,21)(8,20)(9,23)(11,12)(13,26)(14,24)(16,31)(17,30)(18,27)(19,22)(25,33)(28,34)(29,32)

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400603);